Category: Mathematics

Pythagoras Theorem

Pythagoras Theorem: In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Given: A right-angle triangle ABC in which ∠B = 90° To prove: AC2 = AB2 + BC2 Construction: From B draw BD ⊥ AC Proof: In triangles ADB and ABC, we have∠ADB …

Areas of Two Similar Triangles

Areas of Two Similar Triangles: Theorem 1: Prove that the ratio of the areas of two similar triangles is equal to the ratio of the square of any two corresponding sides. Given: △ABC ~ △DEFSo, AB/DE = BC/EF = AC/DFAlso, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F To prove: area △ABC/area △DEF = AB2/DE2 …

Linear Inequations in One Variable

Linear Inequations in One Variable: We know that equations are mathematical statements having two sides connected by a sign of equality. In an inequation, the two sides of the statement are connected by a sign of inequality. The signs of inequality are <, >, ≤, ≥, ≠. Statements like 2x < 3, 12x – 7 ≤ …